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A theory of sets with the negation of the axiom of infinity

✍ Scribed by Stefano Baratella; Ruggero Ferro

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
769 KB
Volume
39
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of a non‐standard development. MSC: 03E30, 03E35.

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